The teeth of conventional gears for handling and transferring torque usually comprise hard and rigid metal, typically steel. Individual teeth are so short along the radii relative to their tangential dimension that tangential deflection is imperceptible.
Teeth on gears usually have a convex shape or profile when intersected by a plane (gear plane) perpendicular to a gear axis about which the gear rotates. Gears in the form of racks do not have an axis per se, but one can envision a similar plane for them as well. The most common type of gear profile has an involute shape that allows the meshing teeth to roll with respect to each other with little or no slipping between the surfaces.
Typically, meshing surfaces of gear teeth make a single line contact between the surfaces of the two meshing teeth because of the convex shapes of the teeth on both gears. Actually, the line of contact has a small effective width due to compression of the material of the two teeth at and adjacent to the theoretical line of contact, and to force that lubricant transmits at the line of contact. Nevertheless, the area of contact between two meshing teeth is very small compared to the total meshing area of the teeth.
When first and second gears are in use to transmit torque between them, it may appear that force transfer occurs between two or more meshing pairs of teeth. Because of unavoidable deviations from the ideal in the gears' shapes, at any given instant a single tooth on each gear transfers almost all of the torque at any given time, or at least much of the time.
The stress generated at the line of contact by the compressive force between the two meshing teeth is called Hertzian contact stress. The force between the two meshing teeth causes high Hertzian contact stress at lines of contact because of the small contact area. Hertzian contact stress limits high-speed torque ratings of most gears used today. All gears can handle less torque at high speeds than at low speeds because of vibration and higher impact loading at higher speeds.
To transmit adequate amounts of torque, gears typically comprise strong materials such as steel. Steel and other strong materials intrinsically have high moduli of elasticity, i.e., are stiff, which means that relatively thick beams, which gear teeth essentially are, deflect very little during operation. Further, stiff materials do not damp vibration well, so conventional gears generate noise and vibration. Conventional rigid gears also resist shock loading poorly.
Gears made of inexpensive plastics having a low modulus of elasticity and low strength compared to metals are much better at damping vibration, but cannot carry much torque. Gears made of plastics reinforced with high-strength fibers have the intrinsic capacity to carry high torque, but they resist Hertzian contact stress poorly.
Some prior art gears have circular rather than involute profiles in an attempt to change the contact area between individual teeth from line to surface. But even circular profiles cannot ensure large surface contact between the gear teeth because their rigidity cannot compensate for inherent misalignments and incompatibilities of various types.
U.S. Pat. No. 4,140,026 describes a gear set having one gear with flexible teeth. The flexible teeth improve torque handling in a gear set having one gear with convex tooth profiles and the other with concave teeth profiles, by shifting the line of contact toward the root of the weaker concave teeth.